Well-Posedness and Exponential Stability of Swelling Porous with Gurtin-Pipkin Thermoelasticity

The focus of this work is to investigate the well-posedness and exponential stability of a swelling porous system with the Gurtin-Pipkin thermal effect as the only source of damping. The well-posedness result is achieved using an essential corollary to the Lumer-Phillips Theorem. By constructing a suitable Lyapunov functional, we establish an exponential stability result without the conventional limitation to the system's parameters (coined a stability number in the literature). Generally, the study demonstrates that the unique dissipation from the Gurtin-Pipkin thermal law is sufficient to stabilize the system exponentially, irrespective of the system's parameters.